If you read the fine details..
Product name: Internal 34W Time Capsule Power supply
Condition: USED, test work
What you are buying is a used power supply that is tested for 10sec to turn on.. NOT GOOD ENOUGH.
Sorry but you could not pay me to take it.. you will need to repair it in no time.. if not 10min after you turn it on and it gets hot and never works again.
Apple used two brands of power supplies.. Flextronics which 80% or so of the early TC got.. combined with lack of cooling and they died after 18months due to Capacitors in the supply overheating.
The other brand was Delta.. far superior design supply.. 90% of gen3 and gen4 TC got Delta supplies.. so what you want is a second hand Gen4 working or not.. they have a soldering fault but the power supplies are very good. Even a gen3 that has had a gentle life would be superior.. there are not many Delta in the supply channels for the obvious reason they don't break down.
I and many others have repair instructions if you want to fix your existing supply.
And as a BTW.. the hard disk could also be dead.. WD black they used in the Gen2 were a poor drive.
https://sites.google.com/site/lapastenague/a-deconstruction-of-routers-and-modems/apple-time-capsule-repair